Hmm, I tried-out a C implementation and the timings weren't bad, 60% slower in exchange for always being correctly rounded.  Do you all think that would be worth it?

# New correctly rounded
$ ./python.exe -m timeit -r11 -s 'from math import hypot' 'hypot(1.7, 15.5, 0.3, 5.2)'
2000000 loops, best of 11: 101 nsec per loop
$ ./python.exe -m timeit -r11 -s 'from math import hypot' 'hypot(1.7, 15.81)'
5000000 loops, best of 11: 82.8 nsec per loop

# Current baseline for Python 3.10
$ ./python.exe -m timeit -r11 -s 'from math import hypot' 'hypot(1.7, 15.5, 0.3, 5.2)'
5000000 loops, best of 11: 65.6 nsec per loop
$ ./python.exe -m timeit -r11 -s 'from math import hypot' 'hypot(1.7, 15.81)'
5000000 loops, best of 11: 56.6 nsec per loop

# Current baseline for Python 3.9
$ ./python.exe -m timeit -r11 -s 'from math import hypot' 'hypot(1.7, 15.5, 0.3, 5.2)'
5000000 loops, best of 11: 72.2 nsec per loop
~/npython $ ./python.exe -m timeit -r11 -s 'from math import hypot' 'hypot(1.7, 15.81)'
5000000 loops, best of 11: 56.2 nsec per loop